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Complexification
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the complexification of a <a href="/facts/Vector_space/M1pxMLx2">vector space</a> <i>V</i> over the field of real numbers (a "real vector space") yields a vector space <i>V</i>C over the <a href="/facts/Complex_number/2w7mqI7e">complex number</a> <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a>, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any <a href="/facts/Basis_(linear_algebra)/89IPoN6c">basis</a> for <i>V</i> (a space over the real numbers) may also serve as a basis for <i>V</i>C over the complex numbers. </p>